Global well-posedness for the 1D cubic nonlinear Schrödinger equation in $L^p,\,p>2$
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910035027689472 |
|---|---|
| author | Hyakuna, Ryosuke |
| author_facet | Hyakuna, Ryosuke |
| contents | In this paper, we show that the one dimensional cubic nonlinear Schrödinger equation is globally well posed in $L^p$ for $2\le p <13/6$. In particular, we prove that the global solution enjoys the persistence property for a twisted variable at any time, which implies the result is a natural exetension of the classical global well-posedness in $L^2$ to $L^p$. The proof exploits the data-decomposition argument originally developed by Vargas-Vega in the functional framework introduced by Zhou. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08554 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global well-posedness for the 1D cubic nonlinear Schrödinger equation in $L^p,\,p>2$ Hyakuna, Ryosuke Analysis of PDEs In this paper, we show that the one dimensional cubic nonlinear Schrödinger equation is globally well posed in $L^p$ for $2\le p <13/6$. In particular, we prove that the global solution enjoys the persistence property for a twisted variable at any time, which implies the result is a natural exetension of the classical global well-posedness in $L^2$ to $L^p$. The proof exploits the data-decomposition argument originally developed by Vargas-Vega in the functional framework introduced by Zhou. |
| title | Global well-posedness for the 1D cubic nonlinear Schrödinger equation in $L^p,\,p>2$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.08554 |